cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A245290 Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are separable in C^2 X C^n as density matrices in quantum mechanics.

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%I A245290 #24 Jul 24 2023 04:53:18
%S A245290 1,31,5119,9961471,259577085951,94554701453852671,
%T A245290 494214691850093043122175,37747948215762478445361018961919,
%U A245290 42694960288928350006693371507341885702143,722273364120299921501331975953872089285372151857151
%N A245290 Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are separable in C^2 X C^n as density matrices in quantum mechanics.
%C A245290 Since separability is not invariant under graph isomorphism, all 2^(n(2n-1))-1 nonzero Laplacian matrices are treated as different.  A nonzero Laplacian matrix different from the complete graph is separable in C^2 X C^n if and only if its complement is.  Since the complete graph is separable, this means that a(n) is odd for all n.
%H A245290 Chai Wah Wu, <a href="http://dx.doi.org/10.1016/j.physleta.2005.10.049">Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices</a>, Physics Letters A, 351 (2006), 18-22.
%H A245290 Chai Wah Wu, <a href="http://arxiv.org/abs/1407.5663">Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics</a>, arXiv:1407.5663 [quant-ph], 2014.
%F A245290 a(n) + A245291(n) = 2^(n*(2*n-1))-1.
%F A245290 a(n) = 2^(n*(n-1))*A229865(n)-1.
%Y A245290 Cf. A245291, A229865.
%K A245290 nonn
%O A245290 1,2
%A A245290 _Chai Wah Wu_, Jul 16 2014